Interfacial Wave Theory of Pattern Formation

Selection of Dendritic Growth and Viscous Fingering in Hele-Shaw Flow

  • Jian-Jun Xu

Part of the Springer Series in Synergetics book series (SSSYN, volume 68)

About this book


The stabiltiy mechanisms of a curved front and the pattern formation in dendrite growth and viscous fingering have been fundamental subjects in the areas of condensed-matter physics, materials science, crystal growth, and fluid mechanics for about half a century. This book studies interfacial instability and pattern formation in dynamic systems away from the equilibrium state. In particular, it deals with the two prominent prototype systems: dendrite growth in solidification and viscous fingering in Hele--Shaw flow. It elucidates the key problems step by step and systematically derives their mathematical solutions, on the basis of the newly established interfacial wave theory. Finally, it carefully examines these results by comparisons with the available experimental results. The unified, asymptotic approach described in this book will be useful for investigation of pattern formation phenomena occurring in a much broader class of inhomogeneous dynamic systems. The results on global stability and selection mechanisms of pattern formation given in this book will be of particular interest to researchers. For the readers who are not familiar with this rapidly growing interdisciplinary field, this book will be a stimulating and valuable introduction.


condensed matter condensed matter physics crystal curvilinear coordinates dendrite growth eigenvalue equilibrium fluid mechanics interfacial instability mechanics pattern formation quantization solution viscous fingering

Authors and affiliations

  • Jian-Jun Xu
    • 1
  1. 1.Department of Mathematics and StatisticsMcGill UniversityMontrealCanada

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 1998
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-80437-3
  • Online ISBN 978-3-642-80435-9
  • Series Print ISSN 0172-7389
  • Buy this book on publisher's site